Offense or resentment taken at a perceived.
Offense or resentment taken at a perceived — often imagined or trivial — slight, most commonly in the phrase “take umbrage.”
About offense taken — wounded pride or the suspicion of having been slighted or snubbed, where the slight is often only supposed, that is, possibly imagined or out of proportion. This separates it from indignation and outrage (moral anger at a genuine wrong, often on others' behalf) and from exasperation, anger, or ire (no necessary slight). Deeper and more brooding than pique (a transient flash of vanity), but more a reaction-in-the-moment than the lasting ill will of resentment. Now largely fixed in the collocation “take umbrage at.”
Early 15c., originally “shadow, shade,” from Old French ombrage, from Latin umbra “shade, shadow” (also the root of umbrella). The emotional sense “suspicion of being slighted” is from the 1610s, from the idea of being “overshadowed”; “take umbrage at” is attested by the 1670s.
A well-sourced development: literal “shade/shadow” (15c.) → “suspicion of being overshadowed” (17c.) → fixed “offense at a slight,” surviving mainly in “take umbrage.” The older literal senses persist only as archaic/literary. No recent-generation shift beyond this long-settled narrowing.